Comments about HW #1 Sunset observations: Pick a convenient spot (your dorm?) Try to get 1 data point per week Keep a lab notebook with date, time, weather, comments Mark down bad weather attempts
Today: Some Physics background Just what you need to know
Isaac Newton (1642-1727) Isaac Newton described the fundamental laws covering the motion of bodies Had to invent his own mathematics (Calculus) to do it! His work is used even today in calculating everything from how fast a car stops when you apply the brakes, to how much rocket fuel to use to get to Saturn! And he did most of it before his 24 th birthday
Newton s First Law An object in uniform motion will stay in motion, an object at rest will stay at rest. If an object s velocity is not changing, either there are no forces acting on it, or the forces are balanced and cancel each other out Hold a ball out in your hand, and note that it is not moving Force of gravity (downward) is balanced by the force your hand applies (upward)! Note: Velocity has a speed (I.e. 60 mph) and a direction (I.e.NW). If an object s velocity is changing, there must be forces present! Dropping a ball Applying the brakes in a car This change can be either speed or direction or BOTH!
Mass and Inertia Mass is described by the amount of matter an object contains. This is different from weight weight requires gravity or some other force to exist! Ex: while swimming, your weight may feel less because the body floats a little. Your mass, however, stays the same! Inertia is simply the tendency of mass to stay in motion Newton s First Law is sometimes called the Law of Inertia:
Acceleration The term acceleration is used to describe the change in a body s velocity over time Stepping on the gas pedal of a car accelerates the car it increases the speed Stepping on the brakes decelerates a car it decreases the speed A change in an object s direction of motion is also acceleration Turning the steering wheel of a car makes the car go left or right this is an acceleration! Forces must be present if acceleration is occurring
Newton s Second Law The force (F) acting on an object equals the product of its acceleration (a) and its mass (m) F = m a We can rearrange this to be: a = F/m For an object with a large mass, the acceleration will be small for a given force If the mass is small, the same force will result in a larger acceleration! Though simple, this expression can be used to calculate everything from how hard to hit the brakes to how much fuel is needed to go to the Moon!
Mass vs Force Mass is measured in Kg in the Metric system (mks) and slugs in the English system. I slug = 32.2 lbs (on Earth) Force is measured in Newtons in mks and pounds in the English system. Why do I know my weight in Kg and in pounds?
Newton s Third Law When two bodies interact, they create equal and opposite forces on each other If two skateboarders have the same mass, and one pushes on the other, they both move away from the center at the same speed If one skateboarder has more mass than the other, the same push will send the smaller person off at a higher speed, and the larger one off in the opposite direction at a smaller speed Why? This works for planets, too!
Circular Motion Tie a string to a ball and swing it around your head Law of inertia says that the ball should go in a straight line Ball goes in a circle there must be forces! Where s the force? It s the tension in the string that is changing the ball s velocity If the string breaks, the ball will move off in a straight line (while falling to the ground)
Centripetal Force If we tie a mass to a string and swing the mass around in a circle, some force is required to keep the mass from flying off in a straight line This is a centripetal force, a m! V = d F C 2 force directed towards the center of the system The tension in the string provides this force. Newton determined that this force can be described by the following equation: m! V d 2 F C =
Conservation of momentum Change in momentum =0 For a closed system p = mv Conservation of Angular momentum Change in Angular momentum =0 For a closed system L = mvr
Definition of Angular Momentum Angular momentum is the rotational equivalent of inertia Can be expressed mathematically as the product of the objects mass, rotational velocity, and radius If no external forces are acting on an object, then its angular momentum is conserved, or a constant: L = m! V! r = constant
Conservation of Angular Momentum Since angular momentum is conserved, if either the mass, size or speed of a spinning object changes, the other values must change to maintain the same value of momentum As a spinning figure skater pulls her arms inward, she changes her value of r in angular momentum. Mass cannot increase, so her rotational speed must increase to maintain a constant angular momentum Works for stars, planets orbiting the Sun, and satellites orbiting the Earth, too!
Orbital Motion and Gravity Astronauts in orbit around the Earth are said to be in free fall, a weightless state. Are they falling? Yes! Imagine a cannon on top of a mountain that fires a cannonball parallel to the ground The cannonball leaves the cannon and is pulled toward the ground by gravity If the ball leaves the cannon with a slow velocity, it falls to the ground near the mountain If the cannonball has a higher velocity, if falls farther from the mountain. What if we gave the cannonball a very large velocity, so large that it misses the Earth? The cannonball would be in orbit around the Earth, and it would be falling!
Newton s Universal Law of Gravitation Every mass exerts a force of attraction on every other mass. The strength of the force is proportional to the product of the masses divided by the square of the distance between them Simply put, everything pulls on everything else Larger masses have a greater pull Objects close together pull more on each other than objects farther apart This is true everywhere, and for all objects The Sun and the planets exert a gravitational force on each other You exert a gravitational force on other people in the room!